13 Chapter Test

Do you know HOW?

Determine whether each function is or is not periodic. If it is periodic, find the period and amplitude.

Find the measure of an angle between 0° and 360° coterminal with the given angle.

3. − 32 ° negative 32 degrees
4. − 229 ° negative 229 degrees
5. 375°

Write each measure in radians. Express your answer in terms of π and also as a decimal rounded to the nearest hundredth.

6. − 225 ° negative 225 degrees
7. 120°
8. 600°

Write each radian measure in degrees. If necessary, round your answer to the nearest degree.

9. 5 π 6 fraction 5 pi , over 6 end fraction
10. − 2 . 5 π negative 2 . 5 pi
11. 0.8

12. Using the graph below, determine how many cycles the sine function has in the interval from 0 to 2π. Find the amplitude and period.

    

Find the amplitude and period of each function. Then sketch one cycle of the graph of each function.

13. y = 4 sin ( 2 x ) y equals 4 sine open 2 x close
14. y = 2 sin ( 4 x ) y equals 2 sine open 4 x close

Solve each equation in the interval from 0 to 2π. Give an exact answer and an answer rounded to the nearest hundredth.

15. cos t = 1 2 cosine t equals , 1 half
16. 3 tan 2 t = 3 3 tangent 2 t equals square root of 3

Graph each function in the interval from 0 to 2π.

17. y = 2 cos x y equals 2 cosine x
18. y = cos ( x + π ) y equals cosine open x plus pi close
19. y = − cos θ π y equals negative cosine , theta over pi
20. y = tan π 3 θ y equals tangent , pi over 3 , theta
21. y = cot x y equals co-tangent x
22. y = sec θ + 1 y equals secant theta plus 1
23. y = csc θ 2 y equals co-secant , theta over 2
24. y = csc ( θ + 1 ) y equals csc open theta plus 1 close

Write an equation for each translation

25. y = cos x , y equals cosine x comma  7.5 units to the right
26. y = sin x , y equals sine x comma  3 units to the left, 1.5 units down

Evaluate each expression. Write your answer in exact form. If the expression is undefined, write undefined.

27. sin 30 ° sine , 30 degrees
28. sin ( − 330 ° ) sine open negative 330 degrees close
29. sec 270 ° secant , 270 degrees
30. tan ( − 60 ° ) tangent open negative 60 degrees close

Do you UNDERSTAND?

31. Open-Ended Sketch a function with period 4 and amplitude 7.
32. Writing Explain how to convert an angle measure in radians to an angle measure in degrees. Include an example.
33. Physics On each swing, a pendulum 18 inches long travels through an angle of 3 π 4  radians . fraction 3 pi , over 4 end fraction . radians , .  How far does the tip of the pendulum travel in one swing? Round your answer to the nearest inch.
34. Reasoning What are the steps you take to find the asymptotes of the function y = tan ( a x + b ) ? y equals tangent open eh x plus b close question mark

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